We characterize the pairs of weights $(v,w)$ for which the operator $Tf(x)=g(x)\int_{s(x)}^{h(x)}f$ with $s$ and $h$ increasing and continuous functions is of strong type $(p,q)$ or weak type $(p,q)$ with respect to the pair $(v,w)$ in the case $0

Keywords:

Hardy--Steklov operator, weights, inequalities Hardy--Steklov operator, weights, inequalities

MSC Classifications:

26D15, 46E30, 42B25 show english descriptions Inequalities for sums, series and integrals
Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Maximal functions, Littlewood-Paley theory 26D15 - Inequalities for sums, series and integrals
46E30 - Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
42B25 - Maximal functions, Littlewood-Paley theory

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